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Properties

Label 1100.2.bt
Level $1100$
Weight $2$
Character orbit 1100.bt
Rep. character $\chi_{1100}(211,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $704$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.bt (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1100 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1100, [\chi])\).

Total New Old
Modular forms 736 736 0
Cusp forms 704 704 0
Eisenstein series 32 32 0

Trace form

\( 704 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} + 166 q^{9} + O(q^{10}) \) \( 704 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} + 166 q^{9} - 20 q^{10} - 14 q^{12} - 10 q^{13} - 3 q^{14} + 3 q^{16} - 10 q^{17} - 25 q^{18} + 3 q^{22} - 10 q^{24} - 18 q^{25} - 34 q^{26} - 10 q^{29} + 5 q^{30} - 30 q^{33} - 4 q^{34} + 18 q^{36} - 2 q^{37} - 31 q^{38} + 30 q^{40} - 2 q^{42} + 23 q^{44} - 20 q^{45} - 5 q^{46} + 12 q^{48} - 160 q^{49} - 40 q^{50} - 25 q^{52} - 38 q^{53} - 30 q^{54} + 22 q^{56} - 20 q^{57} + 18 q^{58} - 40 q^{60} - 10 q^{61} - 105 q^{62} + 35 q^{64} - 33 q^{66} + 65 q^{68} + 10 q^{69} + 35 q^{70} - 75 q^{74} - 144 q^{77} + 20 q^{78} + 128 q^{80} - 140 q^{81} - 10 q^{85} + 17 q^{86} + 67 q^{88} - 12 q^{89} - 100 q^{90} - 76 q^{92} - 18 q^{93} - 120 q^{94} - 115 q^{96} + 18 q^{97} + 35 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1100, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.